Hybrid H∞ state feedback control for discrete-time switched linear systems

Abstract

In this paper, the co-design of continuous-variable controllers and discrete-event switching logics, both in state feedback form, for discrete-time switched linear control systems is investigated. Sufficient synthesis conditions for this co-design problem are proposed here in the form of bilinear matrix inequalities, which is based on the argument of multiple Lyapunov functions. The closed-loop switched system forms a special class of piecewise linear hybrid systems, and is shown to be exponentially stable with a finite l2 induced gain.